Assessment of σ-Diatropicity of the Cyclopropane Molecule

Abstract

Spatial models of the current density field induced in the cyclopropane molecule by stationary, homogeneous magnetic fields, parallel to either the C3 or the C2 symmetry axis, have been constructed. A compact, abridged representation of the models is given via stagnation graphs that convey essential information. Maps of streamlines and moduli are also reported to complete current models that have proven useful to rationalize magnetic tensor properties, that is, magnetizability, 1H and 13C nuclear shieldings, and magnetic shielding along the C3 symmetry axis. Plots of Biot-Savart magnetic shielding density combined with current density visualization yield an accurate, detailed account of the shielding mechanisms. The magnetropicity of the system described by the current density model is fully consistent with the magnitude of magnetic tensors calculated at near Hartree-Fock level. In a field perpendicular to the molecular plane, cyclopropane sustains a diatropic sigma-ring current with the following peculiar features: (i) it follows the molecular periphery rather than the CC framework; (ii) it bifurcates in the proximity of the methylene moieties flowing along the CH bonds, both above and below the sigma(h) plane; (iii) it has an effect on the values of response properties, although it is not as large as expected from naive arguments (e.g., the center-of-mass value of the magnetic shielding constant is dominated by in-plane components rather than the out-of-plane component, which is in contrast to pi-aromatic systems such as benzene); (iv) it has a negligible effect on the strong anisotropy of carbon magnetic shielding, which is shown to arise from local currents. No evidence for strong diatropism, and therefore sigma-aromaticity of the cyclopropane molecule, was found on the magnetic criterion.

Diagnosis of the σ-, π- and (σ+π)-Aromaticity by the Shape of the NICSzz-Scan Curves and Symmetry-Based Selection Rules

“…Moreover, the main feature of the strong diatropic circulation in [c-C 3 H 6 ], which reaches maximal intensity (j max = 0.121 a.u.) outside the line of carbon centers [64,65], accounts well for the slight broadening of the NICS zz -scan curve (halfband width > 3 Å). The calculation of the CMO-NICS zz values for cyclopropane in D 3h symmetry showed that the Walsh orbitals HOMO,-1 (2e′), being σ-type MOs, have positive NICS zz value of 22.2 ppm, the HOMO-2,-3 (1e″), being π-type MOs, have also positive NICS zz value of 8.1 ppm and therefore induce σ-and π-type paratropic ring currents, respectively.…”

“…The CMO-NICS zz results are nicely mirrored on the shape of the NICS zz -scan curve of cyclopropane. It is interesting to notice that Pelloni et al [65] demonstrated that both the large negative NICS value and anisotropies of cyclopropane are mainly determined by the in-plane components rather than the more relevant out-of-plane contribution. The existence of σ-aromaticity in cyclopropane has recently been challenged by ab initio valence bond (VBSCF/cc-PVTZ) computations which revealed directly that the σ-aromatic stabilization energy of cyclopropane is, at most, 3.5 kcal/mol relative to propane [66].…”

Ring current models for acetylene and ethylene molecules

“…The (13s10p5d2f/8s4p1d) uncontracted Gaussian basis set, used in previous near Hartree-Fock (HF) calculations [35,49,50], was employed. For consistency, molecular geometries of acetylene and ethylene were fully optimized at the HF level using the same basis set.…”

“…The interested reader can find details of the computational procedure in these papers [32][33][34][35][36][37][38][39], which demonstrate that the classical formulae, Eqs. (1)-(4), provide practical computational recipes, as well as powerful interpretative tools, useful to rationalize the molecular magnetizability (1) and the shielding of a given nucleus (2) -or equivalently quantities (3) and (4) -via models of the induced current density J B invariant in a gauge translation [40].…”

“…In recent applications [32][33][34][35][36][37][38], the current density vector field is calculated in R 3 by CHF methods relying on an analytical version of the procedure proposed by Keith and Bader [26,27], allowing for a continuous transformation of the origin of the current density that formally sets to zero the diamagnetic contribution (CTOCD-DZ) [39]. The interested reader can find details of the computational procedure in these papers [32][33][34][35][36][37][38][39], which demonstrate that the classical formulae, Eqs.…”